Higher Poisson brackets and differential forms. (English) Zbl 1166.70011

Khudaverdian, H. M.; Voronov, Th. Th.

Kielanowski, Piotr (ed.) et al., Geometric methods in physics. Proceedings of the xxvii workshop on geometric methods in physics, Białowieża, Poland, 29 June – 5 July 2008. Melville, NY: American Institute of Physics (AIP) (ISBN 978-0-7354-0610-0/hbk). AIP Conference Proceedings 1079, 203-215 (2008).

Summary: We show how the relation between Poisson brackets and symplectic forms can be extended to the case of inhomogeneous multivector fields and inhomogeneous differential forms (or pseudodifferential forms). In particular, we arrive at a notion which is a generalization of a symplectic structure and gives rise to higher Poisson brackets. We also obtain a construction of Koszul type brackets in this setting.
For the entire collection see [Zbl 1157.81001].

MSC:

70G45	Differential geometric methods (tensors, connections, symplectic, Poisson, contact, Riemannian, nonholonomic, etc.) for problems in mechanics
70G65	Symmetries, Lie group and Lie algebra methods for problems in mechanics

Keywords:

homotopy Lie algebra; symplectic form; Koszul bracket